Heun Functions - 31.3 Basic Solutions
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 31.3.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HeunHl@{a}{q}{\alpha}{\beta}{\gamma}{\delta}{z} = \sum_{j=0}^{\infty}c_{j}z^{j}}
\HeunHl@{a}{q}{\alpha}{\beta}{\gamma}{\delta}{z} = \sum_{j=0}^{\infty}c_{j}z^{j} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z| < 1} | HeunG(a, q, alpha, beta, gamma, delta, z) = sum(c[j]*(z)^(j), j = 0..infinity)
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Error
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Failure | Missing Macro Error | Manual Skip! | - |
| 31.3.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a\gamma c_{1}-qc_{0} = 0}
a\gamma c_{1}-qc_{0} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a*gamma*c[1]- q*c[0] = 0 |
a*\[Gamma]*Subscript[c, 1]- q*Subscript[c, 0] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 31.3.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{j}c_{j+1}-(Q_{j}+q)c_{j}+P_{j}c_{j-1} = 0}
R_{j}c_{j+1}-(Q_{j}+q)c_{j}+P_{j}c_{j-1} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle j \geq 1} | (a*(j + 1)*(j + gamma))*c[j + 1]-(Q[j]+ q)*c[j]+ P[j]*c[j - 1] = 0 |
(a*(j + 1)*(j + \[Gamma]))*Subscript[c, j + 1]-(Subscript[Q, j]+ q)*Subscript[c, j]+ Subscript[P, j]*Subscript[c, j - 1] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |